It is worth wondering whether or not \(\lbrace Z^{N,x_N}_t,\ 0\le t\le T\rbrace \)  and \(\lbrace Z^{N,x}_t,\ 0\le t\le T\rbrace \) 
are exponentially equivalent, whenever \(x_N\rightarrow x\)  as \(N\rightarrow \infty \) . Indeed, [1]} prove that
property for diffusions with small noise and Lipschitz coefficients, and use it to establish certain results,
of which we shall prove analogs below, but without that exponential equivalence, which fails to hold
in our Poissonian case.
